Tibetan Astro Sciences

1 Basic Principles

The astro sciences of calendar-making, astronomy, astrology, and mathematics touch many aspects
of Tibetan life. Their tradition spread from Tibet to so-called Outer and Inner Mongolia,
Manchuria, East Turkistan, the Russian republics of Buryatia, Kalmykia, and Tuva, and all the other
areas of Tibetan cultural influence in the Himalayas, Central Asia, and present-day China. These
sciences play a significant role in the Tibetan medical tradition. All medical students must study
to a certain level the astro sciences, although astro students are not required to study
medicine.

This topic of knowledge presents the calculations for the ephemeris to give the position of the
planets, as well as those for making the calendar and predicting eclipses. It also includes the
astrological calculations for personal horoscopes and for the information found in the yearly
almanac concerning which days are auspicious or not for starting various activities such as
planting crops. It is a very wide field of study.

There are two divisions: white and black calculations. White and black stand for Indian and
Chinese derived materials in accordance with the predominant color of the clothing traditionally
worn in each country. As is the case with Tibetan medicine, Tibetan astrology shares aspects
similar to those found in Hindu India and China. They are modified and blended, however, and used
in different ways to constitute the unique Tibetan system.

The philosophical contexts of the astro sciences are quite different in the Indian Hindu,
Tibetan Buddhist, and Chinese Confucian worlds. The Tibetan context derives from the
Kalachakra Tantra. "Kalachakra" means "cycles of time." In this tantra, Buddha presented a
system of external, internal, and alternative cycles. The external ones deal with the motion of the
planets through the heavens and various cycles or divisions of time measured by them in terms of
years, months, days, and so forth. The internal ones treat the cycles of energies and breaths
through the body. The alternative cycles consist of the various meditation practices of the tantra
system involving the Buddha-figure called Kalachakra, used to gain control over or purify the
former two cycles.

The external and internal cycles of time parallel each other and occur due to collective
external and individual internal impulses of energy (karma). In other words, there are certain impulses of energy connected with all of us that
drive both the planetary and the human bodily cycles. Since energy and states of mind are closely
related, we can experience the cycles in either a disturbing or a nondisturbing manner. With the
Kalachakra practices, we work to overcome being under the influence of uncontrollably recurring
external and internal situations (samsara) so that, no longer limited or disturbed by them, we are able to realize our
fullest potentials to benefit everyone as much as is possible.

Often, people are under the influence of their personal horoscopes or uncontrollably affected by
the changes of the seasons, the weather, the phases of the moon, or where they are in their own
life cyclesof childhood, adulthood, old age, and so on. They are often also under the influence of
the cycles of energy within their bodies, for instance the menstrual one or the cycle of puberty
through menopause. Such things can cause people great limitations. The Kalachakra system provides a
meditation framework within which we can overcome being under the control of these influences, so
as to overcome the limitations they impose and thus be able to help others the most. The Tibetan
Buddhist system presents astronomy and astrology within this general philosophical framework. It is
quite different from the Hindu Vedic context, in which students learn these sciences to calculate
exact time for performing the Vedic rituals.

In classical Chinese thought, one consults astronomy and astrology in order to maintain
political legitimacy and rule. Confucian philosophy conceives of the emperor as the intermediary
between the heavens and the earth. If the emperor, imperial court, and government act in accord
with the seasons and calendar, and in harmony with the general principles of change in the forces
of the universe, all goes well in the empire. They obviously have the "mandate of heaven." If they
are out of phase, natural disasters occur indicating they have lost their political legitimacy.
Therefore, in order to maintain harmony and keep political power, it is essential to know the exact
times of the seasons and the flow of the universal astrological forces.

Thus, the Chinese philosophical context for astronomy and astrology also differed greatly from
the Tibetan Buddhist framework. Its main purpose was political. Personal horoscopes did not appear
in China until around the eighth century, and that was most probably due to Buddhist influence.

The Indian-derived material in the Tibetan astro sciences comes primarily from two sources, the
Kalachakra or
Cycles of Time Tantra, which is specifically Buddhist, and the
Svarodaya or
Arising from the Vowels Tantra, which has material accepted in common by both the Hindus
and Buddhists.

In connection with the discussion of the external cycles of time,
The Kalachakra Tantra presents the laws of motion of the universe and the calculations for
the ephemeris, calendar, and almanac. Two sets of mathematical formulations developed from it: the
siddhanta or full tenet system, which was lost before it could come to Tibet, and the
karana or precis system.

Between the fifteenth and seventeenth centuries, various Tibetan masters reconstructed the full
tenet system. Thus, Tibetan astro schools currently teach both calculation systems. Even when some
Tibetan lineages favor the full tenet system, they still use the precis system for calculating
solar and lunar eclipses, since it gives better results.

The other source of Indian-derived astro material,
The Arising from the Vowels Tantra, also known as the
Yuddhajaya or
Victory in Battles Tantra, is the only Shaivite Hindu tantra translated into Tibetan and
included in the
Tengyur collection of Indian commentaries. The main feature that derives from it is the
casting of predictive personal horoscopes. In Western astrology, the main emphasis in an individual
horoscope is to look at the natal situation and from that to analyze and describe the personality.
This is not of major interest in the Indian systems, either the Hindu or the Buddhist, although it
is treated. What is of most interest is to chart the unfolding of a person's life.

All Indian astro traditions calculate and analyze a life's course in terms of periods ruled by
nine successive heavenly bodies. The Buddhist system calculates the lifespan from the time of birth
and natal moon position, and then divides it into nine periods according to certain formulas. The
Hindu version does not consider the lifespan. It divides periods according to another rule. In
either case, astrologers interpret each period in relation to its ruling planet, the natal chart,
and the age at which it occurs.

Although Buddhist astrology contains a calculation for people's lifespans, it is not a
fatalistic system of predetermination. It also provides calculations for how far we can extend our
lives if we do many positive, constructive actions. The original Kalachakra system in India
calculated the lifespan with the maximum being 108, whereas the Hindu systems assert the maximum as
120. In Tibet, 108 was reduced to 80 since, according to the Buddhist teachings, the average
lifespan is decreasing in the degenerate age. In the nineteenth century, the Nyingma master Mipam
revised the lifespan calculation so that the maximum is 100. Moreover, regardless of the maximum
age asserted, the Tibetan system contains four different ways to calculate a lifespan. Thus, each
person has many possible lifespans. We are born with many different karmas that could ripen.

Even if we speak of a person having a specific lifespan, extraordinary circumstances can arise
to lengthen or decrease it. If someone is terminally ill, he or she may not have the karmic
potential to recover. Nevertheless, the prayers and ritual ceremonies of a great Lama may act as a
circumstance for deeply buried positive potential for a long life to ripen that ordinarily would
not have surfaced in this lifetime. Likewise, an external event such as an earthquake or war may
provide the circumstance for deeply buried negative potential for a short life to ripen that also
would normally not have come into effect in this life. In such a case, we might die a so-called
"untimely death." In either case, if we do not have the deeply buried potentials, even a dramatic
circumstance in this lifetime will not produce an effect. Special rituals do not benefit some
people, and some individuals survive an earthquake.

A Tibetan horoscope, then, is a general prediction of one possibility that could happen in a
life. There is no guarantee that our lives will actually unfold in that way. There are also other
possibilities, since astrology can predict other lifespans as well. Each possibility resembles a
quantum level. They are all feasible, depending on our actions and practices, as well as on
extraordinary external circumstances. What happens in our lives depends on the karmic potentials we
have built up from previous actions in this and past lifetimes. Otherwise, a human and a dog born
at the same moment and at the same place would experience identical lives.

The main purpose of a Tibetan horoscope is to alert us to possible courses of life we might
experience. Whether or not they turn out to be the case depends on us. Although we have many
potentials, even knowing just one set of them from a horoscope can inspire us to take advantage of
our precious human lives to achieve a spiritual goal. In the context of Kalachakra, we are striving
to overcome all karmic limitations that would prevent us from becoming fully capable of helping
everyone. Meditation on our suffering helps us to develop a determination to be free
(renunciation), as well as compassion for others. Likewise, contemplating the suffering we might
experience in a lifetime as outlined by a horoscope can help us along our spiritual paths. A
Tibetan horoscope, then, can be a skillful means for helping those who are interested in astrology
to progress along the path. A Tibetan horoscope is never a forecast of a predetermined, inherently
true future.

The white calculation system, through its pan-Indic basis, shares certain features in common
with the ancient Greek astro systems. The most prominent example is the division of the zodiac into
twelve signs and houses, with the same names for the signs as the modern Western system uses, but
in Tibetan translation.Thus, natal horoscopes arrange the planets in signs and houses, much as in a
Western chart. The manner of interpretation, however, is very different. As in the Hindu scheme, an
equal-house system is used, the angles between the planets are not considered, and the ascendant is
not a noteworthy point.

The zodiac is the belt through which the sun, moon, and planets rotate around the earth in a
geocentric scheme. For most calculations, this belt is divided into twenty-seven lunar mansions or
constellations rather than into twelve signs. This scheme is not found in the ancient Greek or
modern Western systems, but was shared in common with the classical Hindu ones. Sometimes
twenty-eight constellations are specified, but while the Hindu system would divide the zodiac into
twenty-eight equal portions, the Tibetan system would divide one of the twenty-seven equal portions
into two.

A system of twenty-eight lunar constellations is also found in ancient Chinese astronomy. There,
the emphasis is on the Pole Star as the center of the heavens, like the Chinese emperor. The
mansions, like ministers, rotate around it along the stellar equator and thus consist of slightly
different clusters of stars than are in the pan-Indic mansions. Furthermore, the twenty-eight
Chinese constellations do not make an equal division of the sky.

The Kalachakra system treats ten heavenly bodies, all of which it calls "planets." The first
eight are the sun, the moon, Mars, Mercury, Jupiter, Venus, Saturn and a comet. This last one is
not used in horoscopes. The two remaining heavenly bodies can be referred to as the planets of the
north and south nodes of the moon.

Although the orbits of the sun and the moon are both in the belt of the zodiac, they crisscross
each other. The two points of their intersection are known as the north and south nodes of the
moon. At each new moon, the sun and the moon are roughly conjunct each other, in other words at the
same spot. It is only when this conjunction occurs at either the north or south node, where their
orbits intersect, that the conjunction is exact and a solar eclipse occurs. At full moon, the sun
and the moon are in opposition. When this coincides with one being conjunct the north node and the
other the south, the opposition is exact and a lunar eclipse occurs.

Both the classical Hindu and Kalachakra systems conceive of the north and south nodes of the
moon as planets, whereas the ancient Greek system does not. Both Indian systems explain eclipses as
conjunctions of the sun and moon with the nodal planets.

The Kalachakra system calls the north node planet either Rahu, literally "growler," or the
dragon's head planet, and the south node planet either Kalagni, which means "fire of time," or the
dragon's tail planet. Although the Hindu systems call the former Rahu, they call the latter Ketu,
literally "long tail," referring also to its being the tail of the dragon. According to pan-Indic
mythology, this so-called "dragon" consumes the sun or moon during an eclipse. In Kalachakra,
however, Ketu is the name given to the tenth planet, the comet, which is not included in the
classical Hindu or Greek systems, which treat only nine or seven heavenly bodies respectively.

The classical Chinese system did not include any mention of the north and south nodes of the
moon. The Chinese speak only of the sun, moon, Mercury, Venus, Mars, Jupiter, and Saturn. In later
times, when the concept of the north and south nodes of the moon appeared in Chinese astronomy,
they were referred to as the dragon's head and tail, clearly indicating their Indian origin. They
were not, however, taken as planets.

Another common feature with the ancient Greek and Hindu systems is the naming of the days of the
week after the planets: Sunday for the sun, Monday the moon, Tuesday Mars, Wednesday Mercury,
Thursday Jupiter, Friday Venus, and Saturday Saturn. Because of this, the Tibetan word for weekday
is the same as that for planet.

The Chinese traditionally had a ten-day week and only started using a seven-day one in the
seventh century of the common era, due to the influence of the Nestorian Christian merchant
communities of Persians and Sogdians living in China. The Chinese refer to the days of the week by
their numbers, however, and not by the names of the planets.

One of the major differences between the ancient Greek and Hindu systems concerns the type of
zodiac employed. Like the modern Western system, the ancient Greeks used a tropical zodiac, while
the Hindu systems use a fixed-star or sidereal zodiac. The difference between these two zodiacs
concerns the position of zero degrees Aries. In a tropical zodiac, whenever the sun is at the
vernal equinox in the northern hemisphere, this position is called zero de­grees Aries, regardless
of the position of the sun relative to the constellation Aries at that time. A fixed-star zodiac
labels the sun as being located at zero degrees Aries when the sun actually conjuncts the beginning
of this constellation.

The Kalachakra system criticized the Hindu ones and advocated a tropical zodiac. The Tibetans,
however, discarded this feature of Kalachakra astrology and reverted to a fixed-star system. The
Kalachakra tropical zodiac and the ancient Greek and modern Western ones, however, are not the same
as each other and, similarly, the Hindu and Tibetan fixed-star systems also do not correspond to
each other. The details of these differences are rather complex. To simply the discussion, let us
leave out consideration of the ancient Greek system.

In approximately 290 CE, the vernal equinox point was actually located at the beginning of the
constellation Aries as observed in the sky. Since then, it has been creeping backwards slowly, at a
rate of approximately one degree every seventy-two years. This phenomenon is known as the “
precession of the equinox” – in other words, the backwards motion of the sun’s equinox position.
The discrepancy between the observed position of zero degrees Aries and the position of zero
degrees Aries as defined in terms of the vernal equinox is due to the fact that the earth’s polar
axis gradually rotates in its orientation to the “fixed” stars, with a rotation period of 26,000
years.

The vernal equinox point is now between twenty-three and twenty-four degrees back into Pisces,
the sign immediately before Aries. Thus, the modern Western system currently considers as zero
degrees Aries some point between six and seven degrees in Pisces, as observed in the sky – in other
words, the tropical position minus between twenty-three and twenty-four degrees.

The situation actually is a bit more complicated. There were five different classical Indian
Hindu systems of astrological calculations. The most popular one, still used in India, is that of
the
Surya Siddhanta (The Sun System of Calculations). It considers the position of the vernal equinox point at
approximately 500 CE as being zero degrees Aries, when in fact this position was already a few
degrees into Pisces as observed in the sky. The
Surya Siddhanta then constructs a fixed-star zodiac based on this position of the vernal
equinox as being the start of Aries.

The Indian Hindu systems were aware of the precession of the equinox and gave mathematical
formulas for calculating its value. However, although the discrepancy between the observed position
of Aries and the vernal equinox point increases linearly until the two converge after approximately
26,000 years, the
Surya Siddhanta explains that the discrepancy oscillates. First the vernal equinox point
gradually goes backwards until it reaches twenty-seven degrees behind the originally fixed position
of zero degrees Aries. It then reverses direction and moves forward until it is located
twenty-seven degrees ahead of that set position; whereupon it reverses direction once more until it
reaches the originally fixed position of Aries again. The oscillation then repeats. This
oscillation pattern, then, does not correspond to the actual changing position of the sun at the
vernal equinox in relation either to the position of zero degrees Aries as originally fixed by the
Surya Siddhanta or to the actually observed position of the start of the constellation Aries
in the sky.

The Kalachakra system of astrology criticized the fixed-star zodiac systems used by the
Surya Siddhanta and the four other Indian Hindu systems and the concept of an oscillating
precession of the equinox. It advocated a modified tropical zodiac instead. According to the
Kalachakra system, the vernal equinox point needs to be measured by observation once every sixty
years. That equinox point would then be kept fixed as defining zero degrees Aries for an entire
sixty-year period, and then would need to be corrected at the start of the next sixty-year period.
Moreover, as in the modern Western system, it describes the precession of the equinox as increasing
linearly as it slowly moved backwards around the zodiac, without any oscillation.

When the Kalachakra system went to Tibet in the early eleventh century, however, the Tibetans
stopped making the periodic correction of the vernal equinox point. Consequently, the Tibetan
zodiac system devolved into a fixed-star system, but one in which the discrepancy between its fixed
position of zero degrees Aries and the actual observed position of zero degrees Aries differs from
the discrepancies in any of the Indian Hindu systems. Currently it is approximately thirty-four
degrees.

Observation of the sky reveals that zero degrees Aries of the Western system actually
corresponds to the observed position of the beginning of the constellation Aries minus the
precession factor of between twenty-three and twenty-four degrees. When it shifts into the next
sign back, Aquarius, in about four centuries from now, the so called “New Age of Aquarius” will
tech­nically begin. In common discussion, when people speak of the Age of Aquarius starting very
soon, they are perhaps confusing this with the Chris­tian notion that the change of a millennium
marks a new golden age.

During the Mughal period in India, particularly from the eighteenth century onwards, when
observations of planetary positions became widespread through continuing Arabian astro influences
and contact was made with Western astronomy, many of the Hindu systems discarded the traditional
mathematical models for calculating the positions of not only the sun, but of all the planets. They
saw that the Western models gave more accurate results that could be confirmed through telescopes
and the various heavenly measuring devices that the Mughals built in their observatories. They also
saw that the concept of an oscillating precession of the equinox was incorrect. Therefore, while
keeping a fixed-star zodiac, many therefore adapted the new technique of subtracting a standard
precession value uniformly from the Western-derived tropical zodiac positions of all the planets in
order to derive their positions in the fixed-star zodiac. Each of the Hindu lineages adapted a
slightly different precession value as its conversion factor. The most commonly used one is between
twenty-three and twenty-four degrees, which is the actual observed discrepancy.

Some Hindu astrologers claim, however, that the traditionally calculated planetary positions
give more accurate astrological information. This is a very important point, because Tibetan
astrology is now at the stage at which Hindu astrology was in the eighteenth century when it came
into contact with Western astronomy. The positions of the planets as derived from the mathematical
models of the Kalachakra system also do not correspond exactly to what is observed. Whether it will
be necessary to follow the Hindu example of discarding tradition and using the Western values
modified by the observed precession factor, however, is yet to be decided.

One could argue that it does not really matter what the actual observed positions of the planets
are, because the Tibetan Buddhist astro system was never intended for sending a rocket to the moon
or navigating a ship. The astronomical data is calculated for astrological purposes, and if the
astrological information is empirically accurate and helpful, that is all that matters.

Tibetan astrology is intended to allow us to know our basic karmic situations in life so that we
can work with them to overcome all our limitations and realize all our potentials so as to be of
best benefit to others. It is within this Buddhist context that Tibetan astro studies must be
viewed. It would seem irrelevant to judge and alter it based on its astronomical data not
corresponding to observed planetary positions.

In order to learn and benefit from each other's systems, both Westerners and Tibetans need to
respect the integrity of each other's corpuses of knowledge and wisdom. Ideas can be shared and
indications gained for new areas of research, but it would be tragic to uncritically toss out
traditional approaches and adopt foreign ones. As can be seen from the histories of both Tibetan
medicine and astrology, ideas from foreign cultures were not blindly copied. They stimulated the
Tibetans to work out unique systems of their own, based on their own research and experience, in
which foreign ideas took on new forms. This is the way that progress occurs, for the benefit of
all.

The Chinese-derived black calculations, which are also called element calculations, add a few
more features to the Tibetan calendar, such as correlations with animal and element cycles, like
the year of the iron-horse. They also provide further sets of variables to examine for both
analyzing the personality as well as for making general predictive personal horoscopes. These
features are then integrated with the horoscope information derived from the white calculation
system.

The Chinese-derived material contains calculations for five major areas. The first is for the
basic yearly progressions, to see what will happen during each year of a life. The second concerns
illnesses, determining if harmful spirits caused them and if so, what type of spirit and which
rituals to perform to appease them, as well as predicting how long the illnesses will last. The
third is for the dead, particularly for when and in which direction to remove the corpse from the
house, and what ceremonies to perform to dispel harmful forces. The fourth is calculation of
obstacles, when they will occur in the calendar in general and during a specific person's life. The
fifth concerns marriage, particularly the harmony between the prospective couple. Element
calculations, then, are used primarily for astrological purposes.

As was the case with the Indian-derived material and the Indian Hindu systems, the
Chinese-derived material shares many features in common with the classical Chinese astro schools.
Nevertheless, the way the Tibetans developed and used them has many differences.

The element calculation system correlates the calendar to cycles of sixty years, with each year
ruled successively by one of twelve animals. The classical Chinese order begins with the rat,
whereas the Tibetan sequence starts with the fourth Chinese animal, the hare. Thus, the place in
the sequence at which the sixty-year cycle begins is different.

The list of twelve animals is intertwined with an empowering element for the year, which is one
of the classical Chinese set of five – wood, fire, earth, iron, and water. Each element rules two
years in a row, the first being a male and the second a female year. The Tibetans never use the
Chinese yang and yin. Thus, it takes sixty years for a specific combination to repeat, such as the
wood-male-rat year, for instance, the first in the classical Chinese listing, or the
fire-female-hare year, the first in the Tibetan.

The Tibetan astro system does not employ the classical Chinese system of ten heavenly stems and
twelve earthly branches. The Chinese correlate this with the sixty-year cycle and emphasize it far
greater in their calendar and astrology than the animals and elements.

In addition to a natal combination of animal and element for the year of birth, a progressed
combination is also derived for each year of age, but calculated in different ways for males and
females. In fact, most of the Chinese-derived calculations are different for men and for women. It
should be noted that our age, in both the Tibetan and Chinese systems, refers to the number of
calendar-years during which we have been alive, regardless of how short that period might be in any
particular year. For example, if someone is born in the Tibetan tenth month of a particular year,
the person is one year of age until Tibetan New Year, and then immediately two years old. This is
because although this person has been alive only three months, this has been during two
calendar-years. Thus, Tibetans all become one year older at Tibetan New Year and do not celebrate
or count birthdays in the Western manner. Tibetan age, then, is not an equivalent concept to the
Western idea of age, which counts the number of full years passed since birth.

Each of the twelve animals in its various combinations with the five elements within a
sixty-year cycle has a set of five associated elements used for what is called pebble-calculations.
There are life-force, body, power or capacity, valley-of-fortune, and life-spirit pebble-elements.
The first four are also found in classical Chinese astrology, where power is referred to as wealth.
Life-spirit or the organizing principle in life (Tib.
bla) is more of a Tibetan concept, found in the native tradition of Bon as well.

Based on the analysis of the relation between the natal pebble-elements and those of any
transiting year, we can tell from the life-force ones about possible danger to the life that year
and from the body ones about health and physical harm. From the power ones we can tell about
success, such as in business, from the valley-of-fortune ones about general fortune and travel, and
from the life-spirit ones about the well-being and stability of our basic organizing principles of
life. If there are difficult relations during that year, religious ceremonies are recommended to
counteract these disharmonies.

Each of the twelve animals also has associated with it three weekdays – a life-force,
life-spirit, and deadly one. For everyone sharing the same natal animal-sign, the first two are
auspicious days of the week, while the latter is not. This is used particularly in medical
astrology for choosing days of treatment.

Magic-squares are also employed, specifically the one in which there is a grid of three by
three, with the numbers one through nine arranged, one in each box, such that whether one adds
horizontally, vertically, or diagonally, the sum of any line is fifteen. The nine numbers combine
with the sixty-year cycle so that every 180 years the same magic-square number will correlate with
the same element-animal year. The sequence begins with the number one, and then proceeds in reverse
order: nine, eight, seven, and so on. Each of the nine magic square numbers is correlated with a
color and each of those to one of the five Chinese elements. The numbers are usually referred to in
conjunction with their color. One-white is iron, two-black water, three-navy-blue water, four-green
wood, five-yellow earth, six-white iron, seven-red fire, eight-white iron and nine-maroon or
sometimes nine-red fire. When the magic-square is printed, the color of each box is in accordance
with this scheme.

4

(green)

9

(maroon)

2

(black)

3

(navy blue)

5

(yellow)

7

(red)

8

(white)

1

(white)

6

(white)

From the natal number, a progressed magic-square number is derived for each year of age. As
with the progressed element- animal combination, the calculation is different for males and
females. Each natal square number has an interpretation, which includes a description of past
lives, with their residue propensities in this life, as well as the probable next future life
together with religious ceremonies and statues to commission in order to improve it, and what type
of rebirth might then be possible. This is the source, then, for information on past and future
lives given in Tibetan horoscopes. Body, life-force, power, and valley-of-fortune magic-square
numbers can also be calculated and examined, as is done with the elements.

The eight trigrams of the
I Ching or
Book of Changes – three lines, unbroken or broken, arranged horizontally – are also used
in Tibetan element or black calculations, though never the sixty-four hexagrams. A progressed
trigram for each year of age is derived from a certain arrangement of the trigrams. The calculation
is different for males and females. Everyone of the same gender has the same progressed trigram for
the same age.

Except for the Bon variation of Tibetan astrology, there are no transiting annual trigrams,
which would entail each calendar-year in general being assigned one in a particular sequence. The
natal trigram, then, for both males and females is not calculated from their years of birth, but
rather is taken as their mother's progressed trigram for her age at the year she gave birth to
them. The interpretation of the natal and progressed trigrams gives further information for the
predictive horoscope.

In addition, body, life-force, power, and valley-of-fortune trigrams can be calculated as well,
and these are derived from the four types of magic-square numbers calculated from the natal number.
These four trigrams, as well as the body, life-force, power, and valley-of-fortune natal
pebble-elements of a prospective couple are what are compared in the marriage calculations to
determine compatibility.